Question

Solve each equation you must use

Answer 1

1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.

2)The solution for b² - 4b + 4 = 0 is x=2.

Step-by-step explanation:

The general form of quadratic equation is ax²+bx+c = 0

where

• a is the coefficient of x².
• b is the coefficient of x.
• c is the constant term.

To find the roots :

• Sum of the roots = b
• Product of the roots = c

1) The given quadratic equation is m² - 5m - 14 = 0.

From the above equation, it can be determined that b = -5 and c = -14

The roots are -7 and 2.

• Sum of the roots = -7+2 = -5
• Product of the roots = -7$\times$2 = -14

The solution is given by (x-7) (x+2) = 0.

Therefore, the solutions are x=7 and x= -2.

2) The given quadratic equation is b² - 4b + 4 = 0.

From the above equation, it can be determined that b = -4 and c = 4

The roots are -2 and -2.

• Sum of the roots = -2-2 = -4
• Product of the roots = -2$\times$-2 = 4

The solution is given by (x-2) (x-2) = 0.

Therefore, the solution is x=2.